The ages of Hampton's five cousins are listed below. 15 | 20 | 5 | 13 | 16 | 1) Calculate the mean. 14 2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences. 15 20 5 0- 13 16 -" 15-13 3) Calculate the population standard deviation (a). Σ(x-μ)² N Σ(x-μ)²- (2-μ)² (Please round your answer to two decimal places)
The ages of Hampton's five cousins are listed below. 15 | 20 | 5 | 13 | 16 | 1) Calculate the mean. 14 2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences. 15 20 5 0- 13 16 -" 15-13 3) Calculate the population standard deviation (a). Σ(x-μ)² N Σ(x-μ)²- (2-μ)² (Please round your answer to two decimal places)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**The ages of Hampton's five cousins are listed below:**
- 15
- 20
- 5
- 13
- 16
**1) Calculate the mean (μ):**
The mean is calculated as:
\[ \mu = 14 \]
**2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences.**
| \( x \) | \( x - \mu \) | \( (x - \mu)^2 \) |
| --- | --- | --- |
| 15 | 15 - 14 = 1 | 1^2 = 1 |
| 20 | 20 - 14 = 6 | 6^2 = 36 |
| 5 | 5 - 14 = -9 | (-9)^2 = 81 |
| 13 | 13 - 14 = -1 | (-1)^2 = 1 |
| 16 | 16 - 14 = 2 | 2^2 = 4 |
Summing the squared differences:
\[ \Sigma (x - \mu)^2 = 123 \]
**3) Calculate the population standard deviation (σ):**
The population standard deviation is calculated using the formula:
\[ \sigma = \sqrt{\frac{\Sigma (x - \mu)^2}{N}} \]
Here, \( \Sigma (x - \mu)^2 = 123 \) and \( N = 5 \).
Thus:
\[ \sigma = \sqrt{\frac{123}{5}} \approx 4.95 \]
**(Please round your answer to two decimal places.)**
This page provides a detailed guide for students learning about statistical concepts such as mean and standard deviation, with a practical example involving real data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed7ab37-3726-4b83-a741-6ed60a3ee8a9%2F218ea3e3-79d1-4e0d-badf-1e45099c6183%2Fukqz4cyo_processed.png&w=3840&q=75)
Transcribed Image Text:**The ages of Hampton's five cousins are listed below:**
- 15
- 20
- 5
- 13
- 16
**1) Calculate the mean (μ):**
The mean is calculated as:
\[ \mu = 14 \]
**2) Fill in the table below: Fill in the differences of each data value from the mean, then the squared differences.**
| \( x \) | \( x - \mu \) | \( (x - \mu)^2 \) |
| --- | --- | --- |
| 15 | 15 - 14 = 1 | 1^2 = 1 |
| 20 | 20 - 14 = 6 | 6^2 = 36 |
| 5 | 5 - 14 = -9 | (-9)^2 = 81 |
| 13 | 13 - 14 = -1 | (-1)^2 = 1 |
| 16 | 16 - 14 = 2 | 2^2 = 4 |
Summing the squared differences:
\[ \Sigma (x - \mu)^2 = 123 \]
**3) Calculate the population standard deviation (σ):**
The population standard deviation is calculated using the formula:
\[ \sigma = \sqrt{\frac{\Sigma (x - \mu)^2}{N}} \]
Here, \( \Sigma (x - \mu)^2 = 123 \) and \( N = 5 \).
Thus:
\[ \sigma = \sqrt{\frac{123}{5}} \approx 4.95 \]
**(Please round your answer to two decimal places.)**
This page provides a detailed guide for students learning about statistical concepts such as mean and standard deviation, with a practical example involving real data.
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